Trying to see the 3D Manipulator Widget on selected objects
Is the 3D widget active? Does it show the three icons for move, rotate and scale beside it? If not click on it, or press &#9096; CtrlSpace to toggle it on.

If the widget still doesn't appear on the selected object, it may be that the object's  Origin is somewhere else in the scene. The manipulator will be placed over the origin. If this is the case, go to the Tools tab of the Tools box (press T if the tools box isn't there). You do this in Object mode. About half way down, click on Set Origin, and then Origin to Geometry.

Link to Manual's description of the 3D  manipulator widget.